3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ad523c3f-9109-45a8-8399-80a4c2edeff7-3_513_570_196_625}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure}
A particle of mass \(m\) is suspended at a point \(A\) vertically below a fixed point \(O\) by a light inextensible string of length \(a\) as shown in Figure 2. The particle is given a horizontal velocity \(u\) and subsequently moves along a circular arc until it reaches the point \(B\) where the string becomes slack.
Given that the point \(B\) is at a height \(\frac { 1 } { 2 } a\) above the level of \(O\),
- show that \(\angle B O A = 120 ^ { \circ }\),
- show that \(u ^ { 2 } = \frac { 7 } { 2 } g a\).